Problem: Solve for $x$ and $y$ using elimination. ${-4x-3y = -40}$ ${3x+3y = 36}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $-x = -4$ $\dfrac{-x}{{-1}} = \dfrac{-4}{{-1}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {-4x-3y = -40}\thinspace$ to find $y$ ${-4}{(4)}{ - 3y = -40}$ $-16-3y = -40$ $-16{+16} - 3y = -40{+16}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 4}$ into $\thinspace {3x+3y = 36}\thinspace$ and get the same answer for $y$ : ${3}{(4)}{ + 3y = 36}$ ${y = 8}$